Question

During each heartbeat, approximately \({\bf{70}}\;{\bf{c}}{{\bf{m}}^{\bf{3}}}\) of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.

Short answer

The power output of the heart is \(1.14\;{\rm{W}}\).

Step-by-step solution

Given Data

The volume is \(V = 70\;{\rm{c}}{{\rm{m}}^{\rm{3}}}\).

The average pressure is \(P = 105\;{\rm{mm of Hg}}\).

The number of beats per minute is \(t = 70\;{\rm{beats/min}}\).

Understanding the relation of power

In this problem, the relation of output power along with the work done and time will be utilized.

Calculating the power output of the heart

The relation of power output is given by,

\(\begin{array}{l}{P_0} = \frac{W}{t}\\{P_0} = \left( {\frac{{PV}}{t}} \right)\end{array}\)

Here, \(W\) is the work done.

On plugging the values in the above relation,

\(\begin{array}{l}{P_0} = \left( {\frac{{\left( {105\;{\rm{mm of Hg}} \times \frac{{133\;{\rm{N/}}{{\rm{m}}^{\rm{2}}}}}{{1\;{\rm{mm of Hg}}}}} \right)\left( {70\;{\rm{c}}{{\rm{m}}^{\rm{3}}} \times \frac{{{{10}^{ - 6}}\;{{\rm{m}}^{\rm{3}}}}}{{1\;{\rm{c}}{{\rm{m}}^{\rm{3}}}}}} \right)}}{{\left( {\frac{1}{{70}}\;{\rm{min}} \times \frac{{60\;{\rm{s}}}}{{\;1\;{\rm{min}}}}} \right)}}} \right)\\{P_0} = 1.14\;{\rm{W}}\end{array}\)

Thus, the power output of the heart is \(1.14\;{\rm{W}}\).